Systems and methods for direct winding cooling of electric machines

ABSTRACT

A system and method for cooling electric machines using direct winding heat exchangers (DWHX) is disclosed. The system can comprise a plurality of DWHXs disposed in thermal communication with a plurality of copper windings in the stator of an electric machine for cooling the plurality of copper windings. The plurality of DWHXs can also be in fluid communication with one or more fluid manifolds for providing coolant to the plurality of DWHXs. The one or more manifolds can be in fluid communication with one or more heat reservoirs for rejecting the heat absorbed by the plurality of DWHXs. The heat reservoir can be an internal system radiator or an infinite reservoir such as a cooling pond. The method can comprise a design tool for optimizing a DWHX cooling system utilizing the internal system radiator or an infinite reservoir, among other things.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims benefit under 35 USC §119(e) of U.S. ProvisionalPatent Application Ser. No. 61/536,326, entitled “Direct Winding heatExchanger” and filed Sep. 19, 2011, which is herein incorporated byreference as if fully set forth below in its entirety.

BACKGROUND

1. Technical Field

Embodiments of the present invention relate generally to systems andmethods for cooling electric machines, and specifically to coolingelectric machines with direct winding cooling.

2. Background of Related Art

The increasing demand for electrical power sources for, for example,hybrid electric vehicle (HEV) and electric vehicle (EV) power trains hascreated a need for high torque density electric machines. In addition toHEV and EV passenger cars, other applications that require high torquedensity machines include, for example and not limitation, off roadconstruction equipment, freight trucks, military ships, and electricactuators for flight control surfaces in aircrafts. Currently, alimiting factor for consistent power output is the thermal degradationof the windings. In other words, the heat in the windings caused bygenerating higher power outputs increases the resistance in thewindings, and melts insulation, among other things.

Conventionally, the techniques employed to improve the thermal transportprocesses in small scale (e.g., less than 100 kW) electrical machineshas been focused on improving the internal and external air flow acrossthe electrical machine. Other methods have attempted to improve flowthrough the machine, but generally rely on conduction to transfer heatfrom the windings to the stator, reducing efficiency.

Direct lamination cooling (DLC), for example, provides cooling bypassing coolant directly through channels in the stator. Unfortunately,this configuration changes the flux paths inside the stator. Inaddition, DLC primarily removes heat from the stator and, thus, relieson conduction from the windings to the stator to cool the windings.Phase change cooling, utilizing the heat of vaporization of the coolant,has been used for the thermal management of large scale electricalmachines (i.e., on the order of several hundred megawatts).Unfortunately, large temperature gradients arise due to the increasedheat transfer from evaporative cooling resulting in poor reliability insmall scale applications. In addition, the design and implementation ofadvanced cooling in electric machines in general, and smaller machinesin particular, is limited.

What is needed, therefore, is an integrated design tool, system, andmethod utilizing advanced cooling techniques. In some embodiments, thesystem should include an integrated thermal model including noveladvanced cooling technologies. The integrated, advanced, thermal modelcan be used in conjunction with optimization techniques to provideimproved systems and methods for electric machines with the novelcooling techniques. In some embodiments, the integrated model, inconjunction with optimization techniques, can be used to access systemsizing and cooling requirements, among other things.

BRIEF SUMMARY

Embodiments of the present invention relate generally to systems andmethods for cooling electric machines, and specifically to coolingelectric machines with direct winding cooling. Embodiments of thepresent invention can comprise a system and method for cooling electricmachines using direct winding heat exchangers (DWHX). In someembodiments, the system can comprise a plurality of DWHXs disposed inthermal communication with a plurality of copper windings in the statorof an electric machine for cooling the plurality of copper windings. Insome embodiments, the plurality of DWHXs can also be in fluidcommunication with one or more fluid manifolds, disposed in the statorof the machine, for providing coolant to the plurality of DWHXs. The oneor more manifolds can, in turn, be in fluid communication with, forexample, one or more heat reservoirs for rejecting the heat absorbed bythe plurality of DWHXs. The heat reservoir can be, for example and notlimitation, an internal system radiator or an infinite reservoir suchas, for example and not limitation, an ocean, lake, or cooling pond.

Embodiments of the present invention can also comprise a method, ordesign tool, for optimizing a DWHX cooling system utilizing, forexample, an internal system radiator or an infinite reservoir. Themethod can optimize design parameters to provide increased efficiencyand torque density. Embodiments of the present invention enable electricmachines with significantly increased torque density, while stillsufficiently managing winding thermal loads.

Embodiments of the present invention can comprise a system for coolingan electric machine comprising a stator and one or more copper windings.In some embodiments, the system can comprising one or more directwinding heat exchangers (DWHX) thermally coupled to the one or morecopper windings. The DWHXs can comprise a coolant reservoir and aplurality of micro-features disposed inside the coolant reservoir.Coolant can then flow through the one or more DWHXs to provide directcooling to the one or more copper windings.

In some embodiments, the coolant reservoir can comprise a meso-channeland at least one of the plurality of micro-features can comprise amicro-hydrofoil. In some embodiments, the plurality of micro-featurescan be arranged in a symmetrical array about the centerline of thecoolant flow. In some embodiments, the coolant reservoir can besubstantially prismatic, and the plurality of micro-features can bedisposed only on one or more of the major sides of the coolantreservoir.

In some embodiments, each of the one or more DWHXs can further comprisea dovetail joint for detachably coupling the DWHX to a non-conductivebulkhead. In some embodiments, the system can further comprise athermally conductive epoxy disposed proximate the one or more DWHXs andthe one or more cooper windings for conducting heat therebetween.

Embodiments of the present invention can also comprise a system forcooling an electric machine comprising a stator, one or more end caps, aframe, and one or more copper windings. In some embodiments, the systemcan comprise one or more direct winding heat exchangers (DWHX) thermallycoupled to the one or more copper windings for providing direct coolingto the one or more copper windings, an inlet plenum in fluidcommunication with the one or more DWHXs for providing coolant to theone or more DWHXs, an outlet plenum in fluid communication with the oneor more DWHXs for removing coolant from the one or more DWHXs, and aheat reservoir, in fluid communication with the inlet manifold andoutlet manifold, for rejecting heat transferred to the coolant from theone or more DWHXs.

In some embodiments, the inlet plenum and the outlet plenum can bedisposed in the one or more side covers. The system can further compriseone or more non-conductive bulkheads for detachably coupling the one ormore DWHXs to the electric machine. In some embodiments, the one or moreDWHXs can be pressed into the one or more non-conductive bulkheads. Insome embodiments, the non-conductive bulkheads can, in turn, be pressedinto the frame.

In some embodiments, the heat reservoir can comprise an integralradiator in fluid communication with the inlet plenum and the outletplenum for shedding heat absorbed by the one or more direct winding heatexchangers (DWHX). In other embodiments, the heat reservoir can comprisea substantially infinite external radiator in fluid communication withthe inlet plenum and the outlet plenum for shedding heat absorbed by theone or more direct winding heat exchangers (DWHX). In some embodiments,the profile of each of the plurality of micro-features can be square,round, or rhomboidal.

These and other objects, features and advantages of the presentinvention will become more apparent upon reading the followingspecification in conjunction with the accompanying drawing figures.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 depicts a sectional view of a direct winding heat exchanger(DWHX) system installed on an electric machine, in accordance with someembodiments of the present invention.

FIG. 2 a depicts a cross-sectional view of the DWHX system, inaccordance with some embodiments of the present invention.

FIG. 2 b depicts another cross-sectional view of the DWHX system, inaccordance with some embodiments of the present invention.

FIG. 3 a depicts a cross-sectional view of a DWHX, in accordance withsome embodiments of the present invention.

FIG. 3 b depicts a cross-sectional view of a DWHX with micro-features,in accordance with some embodiments of the present invention.

FIG. 3 c depicts a perspective view of a DWHX with an inlet and anoutlet, in accordance with some embodiments of the present invention.

FIG. 4 depicts a thermal modeling approach for a parametric half-slotmodel of the stator with nine geometric parameters, in accordance withsome embodiments of the present invention.

FIG. 5 depicts dimension parameters of a micro-hydrofoil array for usewith the system, in accordance with some embodiments of the presentinvention.

FIG. 6 is a graph depicting a fluid temperature profile across aradiator with a fixed ambient temperature, in accordance with someembodiments of the present invention.

FIG. 7 is a flowchart depicting an integrated design tool for a DWHXsystem, in accordance with some embodiments of the present invention.

FIG. 8 a is a graph depicting winding temperature vs. temperaturepenalty function, in accordance with some embodiments of the presentinvention.

FIG. 8 b is a diagram of an electric machine frame with respect toactive length, in accordance with some embodiments of the presentinvention.

FIG. 8 c is a diagram of heat flow in an electric machine frame, inaccordance with some embodiments of the present invention.

FIG. 8 d is a diagram of an electric machine frame with an equivalentframe extension, in accordance with some embodiments of the presentinvention.

FIG. 8 e is a schematic of a thermal circuit for the frame of anelectric machine frame, in accordance with some embodiments of thepresent invention.

FIG. 9 is a graph depicting volume and efficiency vs. change in ambienttemperature (ΔT_(amb)) for an initial sizing case study, in accordancewith some embodiments of the present invention.

FIG. 10 is a graph depicting percentage motor and radiator volume oftotal system volume against ΔT_(amb) for the initial sizing case study,in accordance with some embodiments of the present invention.

DETAILED DESCRIPTION

Embodiments of the present invention relate generally to systems andmethods for cooling electric machines, and specifically to coolingelectric machines with direct winding cooling. Embodiments of thepresent invention can comprise a system and method for cooling electricmachines using direct winding heat exchangers (DWHX). In someembodiments, the system can comprise a plurality of DWHXs disposed inthermal communication with a plurality of copper windings in the statorof an electric machine for cooling the plurality of copper windings. Insome embodiments, the plurality of DWHXs can also be in fluidcommunication with one or more fluid manifolds disposed in the stator ofthe machine for providing coolant to the plurality of DWHXs. The one ormore manifolds can be in fluid communication with, for example, one ormore heat reservoirs for rejecting the heat absorbed by the plurality ofDWHXs. The heat reservoir can be, for example and not limitation, aninternal system radiator or an infinite reservoir such as a coolingpond.

Embodiments of the present invention can also comprise a method, ordesign tool, for optimizing a DWHX cooling system utilizing, forexample, an internal system radiator or an infinite reservoir. Themethod can optimize design parameters to provide increased efficiencyand torque density. Embodiments of the present invention enable electricmachines with significantly increased torque density, while stillsufficiently managing winding thermal loads.

To simplify and clarify explanation, the system is described below as asystem for cooling electric machines and motors. One skilled in the artwill recognize, however, that the invention is not so limited. Thesystem can also be deployed for cooling a variety of electric machinescomprising concentrating windings such as, for example and notlimitation, linear actuators, servomotors, solenoids, transformers,switched and variable reluctance permanent magnet motors, inductionmotors, and relays.

The materials described hereinafter as making up the various elements ofthe present invention are intended to be illustrative and notrestrictive. Many suitable materials that would perform the same or asimilar function as the materials described herein are intended to beembraced within the scope of the invention. The DWHXs are describedbelow as being manufactured from aluminum, for example, but otherthermally conductive materials such as, for example and not limitation,copper, silver, gold, platinum, and thermally conductive polymers couldbe used. Such other materials not described herein can include, but arenot limited to, materials that are developed after the time of thedevelopment of the invention. Any dimensions listed in the variousdrawings are for illustrative purposes only and are not intended to belimiting. Other dimensions and proportions are contemplated and intendedto be included within the scope of the invention.

As discussed above, a problem with conventional cooling systems forelectric machines has been that the systems rely on inefficient methodssuch as, for example, indirect cooling. In other words, instead ofplacing the cooling system proximate the windings of a motor, where amajority of the heat is generated, conventional systems have typicallyrelied on indirect cooling through the stator to remove heat from thesystem. In addition to the inefficiencies that this configurationintroduces, the cooling passages in the stator can also affect motorefficiency by changing the magnetic properties of the stator itself.

Embodiments of the present invention, therefore, can comprise a systemutilizing an advanced cooling technique comprising heat exchangersdisposed proximate the stator windings of an electric machine and amethod for designing same. As shown in FIGS. 1-2 b, embodiments of thepresent invention can comprise a direct winding cooling techniquecomprising a novel enhanced heat exchanger component, or direct windingheat exchanger (DWHX) 125, inserted between the winding bundles 110 onthe stator 105 of an electric machine 100.

In high torque density electric machines, for example, the majority ofthe losses are generated in the windings 110. In conventional machines,this heat is generally dissipated through the stator 105 to the frame107 of the machine where it is simply rejected into the ambient air.Embodiments of the present invention, on the other hand, enable the heatgenerated by the windings 110 to be directly transferred into a passingfluid that is in thermal communication with, for example and notlimitation, an infinite thermal reservoir or to an integral heatexchanger (e.g., liquid-to-liquid) or radiator (e.g., liquid-to-air).Consequently, the temperature of the windings 110 can be maintained veryclose to ambient, lowering resistance. This, in turn, enables asubstantial increase in current while maintaining the thermal integrityof the windings 110 and insulation, among other things.

As shown in FIGS. 1 a-1 c, in some embodiments, the system can comprisean electric machine 100, e.g., a motor or other electric machine withconcentrated windings, comprising a shaft 102, one or more bearings 104,stator 105, a plurality of copper windings 110, one or more permanentmagnets 115, and a rotor 120. In some embodiments, one or more DWHXs 125can be disposed in close proximity to, or in direct contact with, thecopper windings 110. In this manner the DWHXs 125 can remove heatdirectly from the copper windings 110 improving efficiency. In someembodiments, the DWHXs 125 can be inserted into conductive fillerdisposed proximate to, or in contact with, the copper windings 110.

In some embodiments, the DWHXs 125 can be in communication with one ormore inlet plenums 127 a for providing coolant to the DWHXs 125. Theinlet plenum 127 a can, in turn, be in fluid communication with acoolant inlet 129 disposed in the end caps 108 of the machine 100 forproviding coolant to the machine from, for example, an integral radiatoror other coolant source, as discussed below. The DWHXs 125 can also bein communication with one or more outlet plenums 127 b and a coolantoutlet 129 b disposed in the end caps 108 to enable hot coolant to exitthe machine 100 for cooling.

In some embodiments, to minimize the effect of the DWHXs 125 on theelectromagnetic of the machine 100, the DWHXs 125 can be isolated fromthe machine 100 with non-conductive bulkheads 131. In some embodiments,for example, the DWHXs 125 can be pressed into the non-conductivebulkheads 131 which, in turn, can be pressed into the frame 107. Thefluid plenums 127 a, 127 b, on the other hand, can be machined directlyinto the end caps 108, which connect to the fluid loop from the inlet129 a and outlet 129 b ports. In this manner, the DWHXs 125 have aminimal effect on the magnetic flux of the machine 100, in general, andthe stator 105, in particular.

Embodiments of the present invention can also comprise a system andmethod for determining the correct sizing and internal channel designfor the heat exchanger 125, or DWHX 125. A DWHX 125 with smallmicro-channels (hydraulic diameter between 0.1-0.5 mm), for example,provides high heat transfer rates due to its increased surface area, butcan also produce a significant coolant pressure drop. This pressureddrop increases pumping work, which decreases overall system efficiency.A larger meso-channel (hydraulic diameter >0.5 mm), on the other hand,reduces coolant pressure drop, but can dramatically reduces heattransfer rates. The optimal DWHX 125, therefore, should exhibit a lowpressure drop, yet maximize heat transfer.

As shown in FIGS. 3 a-3 c, therefore, in some embodiments, the DWHXs 125can comprise one or more coolant passages, or meso-channels 130. Thechannels 130 can contain a cooling medium, such as, for example and notlimitation, a gas (e.g., air or nitrogen), water, or other liquidcoolant (e.g., ethylene glycol). In some embodiments, the cooling mediumcan be pressurized to, for example, prevent boiling and increase heatrejection. As shown in FIG. 3 c, in some embodiments, the DWHX 125 cancomprise one or more coolant inlets 135 a and outlets 135 b. The coolingpassages 130 in the DWHX 125 can be optimized for cooling and can be,for example, a simple open reservoir, a loop with an inlet and anoutlet, or a serpentine design to increase the surface contact betweenthe heat exchanger 125 and the coolant. Of course, the design of thecooling passage can be customized to the cooling needs of a particularwinding 110 or motor 100, as required. In some embodiments, as discussedbelow, the DWHX 125 can comprise an open meso-channel comprising aplurality of micro-features.

As shown in FIGS. 3 a and 3 b, embodiments of the present invention cancomprise a plurality of micro-features 305 disposed inside ameso-channel 130 to enable reduced pressure drop and increased heattransfer. In some embodiments, micro-features 305 can be disposed in anarray 310 to improve cooling efficiency over, for example, an empty, or“blank,” channel 130. The micro-features 305 can improve the heatrejection provided by the DWHX with reduced increases in pumping losses.The micro-features 305 can comprise a variety of shapes including, forexample and not limitation, square, rhomboidal, or round.

In some embodiments, as shown, the micro-features 305 can be airfoilshaped for improved hydrodynamic efficiency. Each flow channel 310 cancontain, for example, one or more micro-hydrofoil arrays 305 that aresymmetric about the centerline of the flow. These arrays 305 can provideincreased thermal performance with reduced pressure drop as compared to,for example, micro-channels. To a large extent, the geometric dimensionsof the micro-hydrofoil features 305 determine the heat transfercharacteristics and pressure drop, and thus directly affect systemperformance. Of course, the airfoil shape and array configuration can bechanged to suit a particular heat load or channel 130 shape. The effectsof different airfoils and array configurations, therefore, arepreferably captured in the design model for the DWHX electric machine.

In some embodiments, as shown in FIGS. 3 a and 3 c, the DWHXs 125 can besubstantially a rectangular prism with a major side 320 a and a minorside 320 b. In some embodiments, the DWHXs 125 can be relative thin andtall to ease installation in the windings 110. In some embodiments, themajor sides 320 a of the DWHXs 125 can be in contact with the windings110 to provide increased surface contact area. In other embodiments, theplurality of micro-features can be disposed on one or more of the majorsides 320 a of the DWHXs 125. This can provide substantial coolingcapacity, while reducing manufacturing costs somewhat. In otherembodiments, the plurality of micro-features can be disposed on one ormore of the major sides 320 a, the minor sides 320 b, or both of theDWHXs 125.

In some embodiments, the DWHXs 125 can further comprise a dovetail joint325 for connecting the DWHXs 125 to, for example, the non-conductivebulkheads 131. The dovetail joint 325 can enable the DWHXs 125 to beretained in the non-conductive bulkheads 131 and can provide somealignment, if necessary, between the inlet 135 a and outlet 135 b of theDWHX 125 and the inlet 127 a and outlet 127 b plenums. In otherembodiments, the DWHXs 125 can be, for example and not limitation,pressed, soldered, welded, or adhered into the non-conductive bulkheads131.

Dissipating the heat collected in the fluid from the windings 110 isalso a challenge in the design of a DWHX electric machine. This heatrejection can be done with, for example and not limitation, anair-to-water radiator, as in an automobile. In this case, the size ofthe radiator required depends on the temperature of the fluid, thetemperature of the ambient air, the flow rate of the fluid, and the flowrate of cooling air over the radiator, among other things. In otherwords, increasing the fluid temperature and dropping the flow ratedecreases the size of the radiator. If the fluid temperature is toohigh, however, the fluid could boil, creating system instabilities. Insome embodiments, therefore, radiator sizing can be included in thedesign model as well.

Similarly, pump sizing can be an important design issue. A lower flowrate, for example, requires less pumping work leading to a smaller pump.Under these conditions, however, the lower flow rate could again cause,for example, coolant boiling and system instabilities (e.g.,overheating). Conversely, while a large pump (and consequently, largeflow rate) reduces system temperatures. The larger pump also increasessystem size and energy consumption. Embodiments of the presentinvention, therefore, can address DWHX and feature design, radiatorsizing, and pump sizing in an integrated model that balances heatdissipation and pumping losses to provide an optimized system.

Thermal Design

In some embodiments, a parametric, self-meshing, finite-difference (FD)technique can be used to model the spatial thermal response of electricmachines. The parametric technique can calculate, numerically, thetemperature distribution throughout a one-half slot model of the stator.In some embodiments, this technique can begin by distributingcalculation nodes throughout a simplified stator geometry, as seen inFIG. 4, using a “center node” distribution approach expressed in polarcoordinates. In some embodiments, an automated segmentation approach canthen capture the geometry of the stator teeth 405, back iron 410,windings 415, and estimated air 420 resulting from under fill in thewindings.

Many stator geometries nonetheless have features that do not correspondto either a radius or an angle in polar coordinates. In someembodiments, therefore, to create a generic model, the system canrepresent the actual slot geometry by features that do correspond toeither a radius or an angle. This enables any slot geometry to be fullydescribed in a parametric manner using only the nine dimensions (i.e.,R_(frame), R_(outer), R_(stator), R_(winding), R_(foot), R_(inner),θ_(foot), θ_(tooth), and θ_(outside)) as shown in FIG. 4 b. The modelmesh can then be generated and segmented according to these parametricdescriptors for the actual stator slot geometry. The method ofconversion between actual stator slot geometry and the parametricparameters is known.¹ ¹ J. R. Mayor and S. A. Semidey, “Generic electricmachine thermal model development using an automated finite differenceapproach,” 2009 IEEE International Electric Machines and DrivesConference, 2009, pp. 137-143, incorporated herein by reference.

In some embodiments, an energy conservation equation can be written foreach node that accounts for substantially all energy entering, exiting,generated, and stored in the node. These equations can then be solvedsimultaneously using matrix inversion to determine the approximatetemperature at each node. In some embodiments, based on thisinformation, the DWHX 125 can be modeled as a convective boundarycondition. The convective model can then be applied at the boundary ofthe windings in the half slot model as illustrated in FIG. 4. Thetemperature of the fluid can be assumed to be the maximum temperature inthe fluid loop, while the heat transfer coefficient of the DWHX 125 canbe calculated using systems and methods detailed below.

DWHX Selection

The selection of the DWHX geometries, including DWHX micro-featuregeometries, is an important part in the design of a DWHX electricmachine. The micro-features can be relatively simple shapes such as, forexample and not limitation, round, square, or rhomboidal. A rhomboidalshape may be useful, for example, because it is relatively efficienthydrodynamically when compared to, for example, a simple square stud,but is nonetheless relatively simple to manufacture (i.e., it is simplya square turned approximately 45 degrees).

In some embodiments, for improved efficiency, the individualmicro-features can be one or more different micro-hydrofoils. Hydrofoilscan be used to improve hydrodynamic efficiency and reduce pumpinglosses, at the cost of somewhat higher manufacturing complexity. In someembodiments, the appropriate hydrofoil (e.g., a NACA 0040 hydrofoil, orsimilar) can be used and can be described by the characteristicpolynomial for the particular hydrofoil. Of course, the type, size,number, and configuration of hydrofoils can be designed to fit a varietyof applications.

As shown in FIGS. 5 a and 5 b, the hydrofoil array, on the other hand,can be described by the transverse spacing (S_(t)), longitudinal spacing(S_(L)), characteristic length (L_(f)), feature height (H_(f)), andchannel height (H_(ch)). These geometric relationships can bemanipulated to alter thermal performance. A dense packing ofmicro-features, for example, tends to produce high heat transfercharacteristics, but also causes significant coolant pressure drop.Conversely, using a relatively low number of micro-features may notsufficiently improve the heat transfer over a meso-channel alone (i.e.,one with no micro-features).

In some embodiments, therefore, a definition of DWHX efficiency can beused to assess the tradeoff of between heat transfer and pressure drop.This definition compares the thermal and flow performance of amicro-hydrofoil enhanced DWHX to a DWHX with a meso-channel of the samedimensions, but with no micro-features (i.e., a “blank” channel). Thisformulation is shown in (1):

$\begin{matrix}{\eta_{DWHX} = {\frac{h_{hydrofoil}}{h_{blank}} + \frac{\Delta \; p_{blank}}{\Delta \; p_{hydrofoil}}}} & (1)\end{matrix}$

where, h_(hydrofoil) and h_(blank) are the heat transfer coefficients ofthe micro-hydrofoil array and the blank meso-channel, respectively.While, Δp_(blank) and Δp_(hydrofoil) are the pressure drops of themicro-hydrofoil array and the blank meso-channel, respectively. Thus,(2) enables the analysis of the tradeoff between cooling capacity andpumping losses to arrive at an optimized solution for a particularapplication.

Cooling Capacity Design

As discussed above, the cooling capacity of the DWHX increases with thenumber of micro-features, as do the pumping losses. As a result, anoptimized solution, which provides improved cooling capacity and reducedpumping losses, exists for a given set of criterion. These criterion maychange substantially, however, depending on application. The coolingsystem for an electric motorcycle, for example, maybe volume andefficiency limited. In other words, a motorcycle provides limited spacefor the electric machine and requires good efficiency to provide useablerange. A nuclear powered naval ship, on the other hand, has fewer spacerestraints and basically unlimited power and cooling capacity. As aresult, for an attack ship, for example, outright power and speed maytrump space and/or energy efficiency.

The convective heat transfer coefficient for the nominal blankmeso-channel, h_(blank), can be calculated using a standard Nusselt (Nu)correlation for rectangular flow geometries using (2):

$\begin{matrix}{h_{blank} = \frac{{Nu} \cdot k_{fluid}}{D_{h,{blank}}}} & (2)\end{matrix}$

where, Nu is the Nusselt number for the meso-channel, k_(fluid) is thethermal conductivity of the fluid, and D_(h,blank) is the hydraulicdiameter of the meso-channel. The hydraulic diameter of the meso-channelcan be shown by (3):

$\begin{matrix}{D_{h,{blank}} = \frac{4 \cdot H_{ch} \cdot W_{ch}}{{2 \cdot H_{ch}} + {2 \cdot W_{ch}}}} & (3)\end{matrix}$

where, H_(ch) is the height of the meso-channel and W_(ch) is the widthof the meso-channel. The height of the meso-channel can be calculatedfrom (4):

H _(ch) =t _(DWHX)−2·t _(wall)  (4)

where, t_(DWHX) is the overall thickness of the DWHX and t_(wall) is thewall thickness of the DWHX.

Both of these values can be specified by the designer based onmanufacturing and related design considerations. The pressure drop ofthe blank meso-channel can be calculated using the Hagen-Poiseuilledescription of pressure drop through a rectangular channel as shown in(5):

$\begin{matrix}{{\Delta \; p_{blank}} = \frac{L \cdot 12 \cdot \mu \cdot \overset{.}{V}}{H_{ch}^{3} \cdot W_{ch}}} & (5)\end{matrix}$

where, L is the length of the flow channel in the flow direction, μ isthe dynamic viscosity, and {dot over (V)} is the volumetric flow ratethrough the channel. The heat transfer coefficient for themicro-hydrofoil arrays is shown in (6):

$\begin{matrix}{h_{hydrofoil} = \frac{{Nu}_{hydrofoil} \cdot k_{fluid}}{D_{h,{hydrofoil}}}} & (6)\end{matrix}$

The Nusselt number associated with the micro-hydrofoil arrays can becalculated using the known correlations of the hydrofoil characteristicsincluding, S_(t), S_(l), H_(f), and L_(c), as shown in FIG. 5 and theReynolds number, Re, for the micro-hydrofoil array as defined in (7):

$\begin{matrix}{{Re} = \frac{\overset{.}{V} \cdot D_{h,{hydrofoil}} \cdot \rho_{fluid}}{A_{c,{features}} \cdot \mu_{fluid}}} & (7)\end{matrix}$

where, ρ_(fluid) is the density of the fluid.

The hydraulic diameter of the micro-hydrofoil array is defined in (8)and the cross sectional area of the micro-hydrofoil arrays in the flowdirection is defined in (9):

$\begin{matrix}{D_{h,{hydrofoil}} = \frac{4( {{H_{ch} \cdot W_{ch}} - {L_{c} \cdot H_{f} \cdot N_{f}}} )}{{2 \cdot H_{ch}} + {2 \cdot W_{ch}} + {2 \cdot H_{f} \cdot N_{f,t}}}} & (8)\end{matrix}$

where, N_(f,t) is the number of micro-hydrofoil features in thetransverse direction.

A _(c,features) =H _(ch) ·W _(ch) −L _(c) ·H _(f) ·N _(f,t)  (9)

The pressure drop across the micro-hydrofoil array is shown in (10):

$\begin{matrix}{{\Delta \; p_{hydrofoil}} = {\frac{L \cdot f^{*}}{D_{h,{hydrofoil}}} \cdot \frac{1}{2} \cdot \rho_{fluid} \cdot \nu^{2}}} & (10)\end{matrix}$

where, ν is the mean velocity defined as the volumetric flow ratedivided by the cross sectional area of the micro-hydrofoil array in theflow direction. As with the Nusselt number, the friction factor, f*, canbe calculated using known correlations.

The optimal set of micro-hydrofoil array geometries (S_(t)/L_(c),S_(l)/L_(c), and H_(f)/L_(c)) maximizes the DWHX efficiency, as definedin (1). Embodiments of the present invention, therefore, can comprisefirst evaluating the efficiency of all geometry sets that are feasible.Feasibility of a geometry set can be first defined by the feasibleratios of S_(t)/L_(c), S_(l)/L_(c), and H_(f)/L_(c). The feasible ratioscan then be defined as the applicable range of the correlations. Theranges tested herein are shown in Table 1:

TABLE 1 Feasible Micro-Hydrofoil Array Geometric Ratios Ratios Min ValueMax Value S_(t)/L_(c) 1 3 S_(l)/L_(c) 3 5 H_(f)/L_(c) 1 2.5 L_(c) [mm]0.2 1which are representative ratios relatively in the middle of reasonableranges for ease of testing. Of course, these ratios are exemplary onlyand larger ratios are possible. The range for S_(t)/L_(c) can be, forexample and not limitation, between at least 1 and 5. The range forS_(t)/L_(c) can be, for example and not limitation, between at least 2and 6. The range for H_(f)/L_(c) can be, for example and not limitation,between 1 and 10, or larger. Similarly, L_(c) can be, for example andnot limitation, between 0.1 mm and 2 mm.

In some embodiments, the feasibility of the feature height andlongitudinal spacing can be accessed next. In a preferred embodiment,the height of the features is preferably no larger than half of thechannel height to avoid, for example and not limitation, verticalinterference of the features in an aligned array. In a staggered array,on the other hand, the vertical height variation can create a verticaldisturbance to the fluid that may impart additional flow losses. Inaddition, the longitudinal spacing, S_(l), is preferably large enough toprevent the hydrofoils from overlapping in the longitudinal direction.These two constraints are shown in (11) and (12), respectively.

$\begin{matrix}{H_{f} < \frac{H_{ch}}{2}} & (11) \\{S_{l} > {c + S_{t} - L_{c}}} & (12)\end{matrix}$

where c is the length of the chord of the hydrofoil (i.e., thecharacteristic length divided by the thickness ratio).

The efficiency of each feasible geometry set can then be calculated.Following this calculation, the maximum efficiency from the all feasiblegeometry sets can be identified. The geometry set with the maximumefficiency can then be determined. The thickness of the DWHX, t_(DWHX),and the thickness of the wall, t_(wall), are determined by the designerbased on electromagnetic design and manufacturing considerations, asdiscussed below.

Pumping Power

The volume of the radiator and the pump is another important systemdesign component. The temperature drop across the radiator isillustrated in FIG. 6. As shown, the fluid temperature approaches theambient temperature as the fluid travels along the length of theradiator. At steady state, assuming proper radiator sizing, thetemperature drop across the radiator is equal to the temperature riseacross the DWHXs in the machine. The temperature rise across the DWHXsin the machine is a function of the loss in the machine and the flowrate through the system. Ideally, of course, the radiator should providethe required cooling capacity at the minimum pumping loss. For ease ofcalculation, and to provide a margin of safety, the maximum fluidtemperature in the DWHXs, therefore, is considered to be the inlettemperature to the radiator.

A convenient way to define the size of the radiator is by specifying twotemperature differences. The first is the temperature difference fromthe outlet of the radiator to the ambient temperature, ΔT_(amb). Thesecond is the temperature increase across the DWHXs, ΔT_(DWHX). FromΔT_(DWHX), the mass flow rate through the system can be calculated using(13).

$\begin{matrix}{\overset{.}{m} = \frac{P_{copper}}{C_{p,{fluid}}\Delta \; T_{DWHX}}} & (13)\end{matrix}$

where, C_(p,fluid) is the specific heat of the fluid. Of course, thisformulation assumes that all of the copper loss, P_(copper), goes intoheating the fluid. For a specific example, one can use manufacturer'sdata regarding the thermal resistance per unit volume of the radiatorcan be calculated from mass flow rate as shown in (14):

R _(rad)′″=0.0199·exp(−21.437·{dot over (m)})+0.03898  (14)

which can be derived empirically from, for example, experimental ormanufacturer's data² for a particular forced cooled air exchanger, forexample. Of course, other types of heat sinks such as differentradiators or heat exchangers can be similarly derived. The volume of theradiator can then be calculated using (15): ² In this case, the formulawas derived from manufacturer's data. See, “MCRX20-QP Radiator Series”,Rouchon Industries, Inc. (2012), available at http://www.swiftech.com/MCRX20-QP-RADIATOR-SERIES.aspx#tab2

$\begin{matrix}{V_{rad} = \frac{P_{copper} \cdot R_{rad}^{m}}{\Delta \; T_{lm}}} & (15)\end{matrix}$

where the log mean temperature, is defined in (16):

$\begin{matrix}{{\Delta \; T_{lm}} = \frac{( {T_{out} - T_{\infty}} ) - ( {T_{in} - T_{\infty}} )}{\ln ( {( {T_{out} - T_{\infty}} )\text{/}( {T_{in} - T_{\infty}} )} )}} & (16)\end{matrix}$

where, the inlet and the outlet temperatures are defined in (17) and(18), respectively:

T _(in) =T ₂₈ +ΔT _(DWHX)  (17)

T _(out) =T _(∞) +ΔT _(amb)  (18)

where T_(∞) is the ambient temperature. The size of the pump is a linearfunction of the required pumping power as defined in (19):

V _(pump)=8.8642e−4·P _(pump)  (19)

which, like (14) can also be derived empirically from, for example,experimental or manufacturer's data. Of course, as with radiators, pumpsof different types and sizes can be separately derived and thecalculations provided herein are intended to be purely illustrative. Insome embodiments, the pumping power can be calculated using (20):

$\begin{matrix}{P_{pump} = \frac{{\overset{.}{V} \cdot \Delta}\; p}{\eta_{pump}}} & (20)\end{matrix}$

where Δp is the pressure drop through the system and η_(pump) is theefficiency of the pump. The pressure drop through the system can thencalculated using (21):

Δp=(Δp _(rad) +Δp _(DWHX) ·Nm)·η_(minor)  (21)

where Δp_(rad) is the pressure drop through the radiator, Nm is thenumber of stator slots, and η_(minor) is the minor loss coefficient. Inother words, the coefficient accounts for substantially all of the minorpressure losses through the system. Similarly, the pressure drop throughthe radiator is calculated using (22):

Δp _(rad)=(0.1314·(60.3·{dot over (m)})²+0.501)·V _(rad)  (22)

which, as before, was derived from manufacturer's data.

These equations tend to indicate that the volume of the radiator andpump are largely functions of ΔT_(amb), ΔT_(DWHX), and T_(∞), whereT_(∞) is a constraint based on the specification of the designer.

Method for Optimization of Design

The electromagnetics of an electric machine require the selection of avariety of design parameters such as, for example and not limitation,stator bore diameter, air gap length, and slot fill factor. As discussedabove, the thermal design of the electric machine, on the other hand,requires the selection of, among other things, ambient temperature, thethickness of the DWHX, DWHX wall thickness, and the temperaturedifferences ΔT_(amb) and ΔT_(DWHX). The ambient temperature, T_(∞), forexample, can be selected by the designer based on desired operatingconditions. This can be based on, for example and not limitation, thedesired installation location, material properties, or desired output.In other words, T_(∞) can be chosen to prevent, for example and notlimitation, coolant boiling, burns to users, overheating of the electricmachine in a confined space, or to prevent winding, stator, or framemeltdown.

As mentioned above, the selection of DWHX thickness and wall thickness,on the other hand, are based largely on design choices based largely onthe manufacturability of the heat exchanger and/or electromagneticconsiderations. Electromagnetically, the optimal DWHX would have minimalthickness. Thus, the thicknesses are preferably minimized based onmanufacturability and/or durability. ΔT_(amb) and ΔT_(DWHX) areparameters that can significantly affect system size and, thus, arepreferably optimized.

Embodiments of the present invention, therefore, can comprise anintegrated design tool. An integrated design simulation is illustratedin FIG. 7. The integrated model includes inputs and outputs 710 a, 710b; optimization constraints 705 a, 705 b, 705 c, 705 d (i.e.,constraints that are determined by the designer); DWHX, radiator, andpump sizing modules 715; and the DWHX electric machines thermalsimulation 720. The integrated model also includes a system thermalsimulation 725.

Optimization can begin with the formulation of an objective function.The objective function can be determined based on design parameters forthe electric machine. In some embodiments, such as in a racingapplication, the electric machine can be optimized for maximum output.For use in an EV, on the other hand, the electric machine can beoptimized to minimize volume and/or maximize efficiency (e.g., range).

In some embodiments, the fitness function can maximize torque density.The fitness function for torque density, f, can be derived as shown in(23). This formulation considers the tradeoff between torque density(Nm/L) and system efficiency, among other things:

$\begin{matrix}{f = {{( {1 - \frac{\rho_{torque}}{\rho_{torque}^{*}}} ) \cdot 100} + {( {1 - \eta_{system}} ) \cdot 100} + \varphi_{tot}}} & (23)\end{matrix}$

where ρ_(torque)* is a desired torque density, ρ_(torque) is the torquedensity if the system, η_(system) is the system efficiency, and φ_(tot)is the sum of all penalties. The torque density of the system,therefore, can be defined in (24):

$\begin{matrix}{\rho_{torque} = \frac{T}{V_{rad} + V_{pump} + V_{motor}}} & (24)\end{matrix}$

where T is the torque produced by the machine. The system efficiency canbe calculated using (25):

$\begin{matrix}{\eta_{system} = \frac{P_{out}}{P_{out} + P_{pump} + P_{core} + P_{copper}}} & (25)\end{matrix}$

where P_(out) is the designed output power and P_(core) is the coreloss. The penalties can be calculated using (26):

φ_(tot)=10,000(φ_(sat)+φ_(dmgr)+φ_(dmgs)+φ_(temp))  (26)

where φ_(sat) is the penalty for armature reaction, φ_(dmgr) is thepenalty for demagnetization at a rated condition, φ_(dmgs) is thepenalty for demagnetization for a shorted condition, and φ_(temp) is thepenalty for insulation life.³ The penalty function for temperature risecan be defined as: ³ The formulation of these penalties can be found in:S. A. Semidey, D. Yao, J. R. Mayor, R. G. Harley, and T. G. Habetler,“Optimal Electromagnetic-Thermo-Mechanical Integrated Design CandidateSearch and Selection for Surface-Mount Permanent-Magnet MachinesConsidering Load Profiles,” Industry Applications, IEEE Transactions on,vol. 47, pp. 2460-2468, 2011, incorporated herein by reference.

$\begin{matrix}{\varphi_{temp} = {\max ( {\frac{L_{EX} - L_{T}}{L_{EX}},0} )}} & (27)\end{matrix}$

where L_(EX) is the expected winding insulation life. As shown in FIG.8, for example, if a class B winding insulation is used and the expectedinsulation life is 20,000 hours, the value of φ_(temp) is plotted whereL_(T) is defined by (28):

L _(T)=10000·10^(−0.03(T−140))  (28)

where T is the maximum insulation temperature for the thermalsimulation. Of course, the fitness function would be different for adifferent set of criterion (e.g., absolute power or maximum efficiency)and is contemplated herein.

Optimization Case Studies

Two case studies were performed to assess sizing of a DWHX electricmachine. The first case study, or integrated radiator case study, wasused to understand the tradeoffs between motor sizing and radiatorsizing. This analysis could be useful for determining a system foroptimizing torque within a specific volume, for example. The second casestudy, or infinite reservoir case study, was performed to assess thesize of the DWHX electric machine when considering an infinite thermalreservoir such as, for example and not limitation, a cooling pond,river, or the ocean. This could be useful in applications, such asoffshore racing boats, where ultimate power is the goal, as opposed toefficiency, and there is an essentially limitless heat sink (e.g., theocean or a lake).

Implementation of Optimization Technique

The integrated model can be combined with an optimization technique toperform case studies. Several nonlinear global optimization techniquescan be used to find the optimal DWHX electric machine geometries suchas, for example and not limitation, simulated annealing, evolutionaryalgorithms, and branch and bound. Due to the non-linearity of theelectromagnetics of electric machines and some discontinuous variablesfor describing same, potential optimization techniques may be somewhatlimited to techniques such as, for example and not limitation, particleswarm optimization (PSO) and genetic algorithms (GA), though PSOprovides a slight advantage to GA is some cases.

Optimization Specs

The specifications for the DWHX electric machine in each case study aresummarized in Table 2:

TABLE 2 DWHX Electric Machine Specification List Specification ValueUnits Power 20 kW Speed 3600 RPM Torque 53 N-m Voltage 240 VAC T_(inf)25 C Desired Torque 10 N-m/L Density Frame Material Aluminum —

The key specifications for this case are 20 kW of power at 53 N-m withan ambient temperature of 25° C. Several key parameters can bedetermined by the designer as previously identified. The constraintsused in the two case studies are presented in Table 3:

TABLE 3 DWHX electric machine optimization constraints Constraints ValueUnits t_(wall) 0.5 mm t_(DWHX) 2 mm t_(frame) 3 mm k_(windings) 32.5W/m-k Contact Resistance 0.001 m²-K/W Fill Factor 0.75 — Number of Poles4 — Slots per phase per pole 1 — Air Gap Length 0.4 mm Saturation 2.4 T

The first five constraints are thermal-mechanical constraints. The walland overall thickness of the DWHX were set based on knownmicro-manufacturing limits.

Frame Thickness

In some embodiments, the thickness of the frame can be used to increasethe ambient rejection area of the machine. A two dimensional approachfor the frame thickness can simplify the required computation, but tomaintain the accuracy of the model, the three-dimensional thermaleffects are preferably captured. In other words, as shown in FIG. 8 b,the model should account for heat transfer in the Z direction as well asthe R direction. The most significant heat transfer in the Z direction,therefore, takes place in the frame.

In addition, also as shown in FIG. 8 b, the frame area of the machine issignificantly larger than the active length area (i.e., the areaapproximated by the stator and rotor) and thus is preferably accountedfor in the boundary condition for the two dimensional model.Unfortunately, a straight area multiplier would lead to over predictionof cooling capabilities because the temperature along the frame is notuniform (i.e., it is higher along the active length). It is moreaccurate, therefore, to describe the frame as a fin, or triangle, whichtends to account for the temperature drop from left to right (as shown)across the frame.

The heat flow through the frame of the machine can be illustrated as inFIG. 8 c. Notice that there are two heat flows. The first heat flow isfrom the active length and the second into the end caps, which can berepresented as an extension of the frame, L_(extension), as seen in FIG.8 d. L_(extension) can now be modeled as an annular fin and thetemperature drop across L_(extension) can be accounted for using classicfin theory.

The heat flow through the frame, therefore, can be represented as athermal circuit as seen in FIG. 8 e. Notice that in FIG. 8 e the secondheat flow has a fin efficiency associated with the L_(extension). Theefficiency accounts for the temperature drop along the length of thefin. Fin efficiency can be calculated using standard analyticalsolutions. The thermal circuit can then be solved and applied as athermal resistance boundary condition thus accounting for the framethree-dimensional effects.

Frame capacitance, therefore, can be represented by (29):

$\begin{matrix}{{\hat{\rho}}_{frame} = \frac{m_{{tot},{frame}}}{V_{{frame},{{active}\mspace{14mu} {length}}}}} & (29)\end{matrix}$

In other embodiments, because of the cooling capabilities of the DWHXelectric machine, the extra cooling area for the frame is not needed. Asa result, the frame thickness can simply be set by known manufacturinglimits such as, for example and not limitation, material strength orthermal properties.

Windings

Generally, the effective thermal conductivity of the windings is low (<1W/m-k) because of a low thermal conductivity filler material (e.g.,air). For the case studies, however, a filler material of thermallyconductive epoxy is used with a thermal conductivity of 5 W/m-k. Ofcourse, other thermally conductive materials could be used and arecontemplated herein. This enables a relatively high packing factor ofapproximately 0.75. The contact resistance between the heat exchangerand the coil can be set as a conservative estimate from typical values.

The optimization variables are discussed above. The optimizationvariable domains used in the case studies are presented in Table 4:

TABLE 4 DWHX electric machine optimization domain Variable Domain UnitsD 30-100 mm L 30-100 mm h_(m) 5-15 mm J 5-30 A/mm² ΔT_(DWHX)  .1-110 °C. ΔT_(amb) 10-110 ° C.

Note that the current densities in conventional electric machinestypically range from approximately 3-12 A/mm², but the DWHX coolingtechnique enables much higher current densities. The domain for theheight of the magnets was set based on typical magnet sizes.

Example 1 Integrated Radiator

In many applications, the total system volume is critical. This can bedue to, for example and not limitation, size or weight constraints,power requirements, or cost. A propulsion system for an electric car ormotorcycle, for example, is preferably powerful, efficient, andrelatively small. As a result, the electromagnetic, total motor,radiator, and pump volume all should be considered. This case study wasperformed, therefore, to understand the tradeoffs between total motorvolume, radiator volume, total system volume, and torque. This tradeoffcan be conveniently assessed using torque density, or the amount oftorque available per unit volume.

In this case study, the temperature difference from the outlet of theradiator to the ambient (ΔT_(amb)) was fixed between 10° C. and 110° C.An optimization was then performed at the fixed ΔT_(amb) and the otheroptimization variables were optimized. This was performed for a range ofΔT_(amb) starting at 10° C. and ending at 110° C. The optimization wasreplicated three times for each ΔT_(amb) to ensure the optimal solutionwas found. The results from the case study are displayed in FIG. 9,which shows the volume on the left hand axis and the efficiency on theright hand axis for each fixed ΔT_(amb).

As shown in FIG. 9, as ΔT_(amb) increases, the system volume decreasesuntil ΔT_(amb) reaches 100° C., at which time the system volume beginsto increase. It should be noted that the driving force for radiator heatrejection is ΔT_(lm), which was defined in (18), and the inlettemperature to the radiator is determined by the thermal limit of thewindings. As ΔT_(amb) increases, therefore, Δ_(lm) increases until thethermal limit of the windings is reached leading to the inflection at100° C. Also, notice the radiator volume is a weak function of ΔT_(amb)between 10° C. and 80° C. and the efficiency of the machine trends withthe volume of the motor, as expected.

The fitness function values for each of the optimization trials areshown in Table 5:

TABLE 5 Fitness Function values for each trial in radiator case studyΔT_(amb) Trial 10 20 30 40 50 60 70 80 90 100 110 # Fitness FunctionValue 1 −55.8 −66.6 −75.9 −83.0 −88.4 −97.1 −107.8 −112.7 −124.9 −123.1−112.8 2 −55.1 −66.7 −75.9 −83.1 −88.4 −98.3 −104.8 −117.4 −124.9 −123.1−110.5 3 −55.7 −66.7 −75.8 −82.1 −88.4 −98.3 −107.3 −117.4 −123.9 −123.1−111.8

The optimization was run several times to ensure the global minimum wasreached. For each of the optimization trials the fitness function waswithin three points of the other trials.

The result from each optimization for the best case for each isdisplayed in Table 6:

TABLE 6 Optimization Results for all cases from the ΔT_(amb) initialsizing case study ΔTamb 10 20 30 40 50 60 70 80 90 100 110 D [mm] 87.985.6 86.1 86.2 87.2 87.7 84.6 85.9 88.5 81.1 83.5 L [mm] 38.9 40 37.536.6 33.5 30.8 34.5 30 27.7 40 40.9 J [A/mm2] 6.7 9.1 8.7 10 10.1 10.413.5 14.1 9.6 12.7 10 ΔTDWHX 104.3 89.1 76.6 65.8 52.2 2 2.2 2.6 2.2 1.71.2 EM Torque 47.4 53.1 55.4 55.9 59.0 62.5 66.1 72.5 66.8 61.6 53.2Density [N-m/L] Total 15.9 17.1 18.1 18.7 19.4 20.4 21.3 22.5 23.2 22.921.8 Torque Density [N-m/L] Efficiency 0.96 0.95 0.95 0.95 0.95 0.940.93 0.92 0.93 0.94 0.95 Fitness −55.8 −66.6 −75.9 −83.0 −88.4 −98.3−107.8 −117.4 −124.9 −123.1 −112.8 Value

As shown, the optimal DWHX electric machine based on the constraints andfitness function previously defined is located at a ΔT_(lm) of 90° C. Atthis condition the torque density of the system is 23.2 N-m/1 and thetorque density based on electromagnetic volume is 66.8 N-m/L. Note thatthe maximum torque density based on electromagnetic volume is 72.5 N-m/Land happens at a ΔT_(lm) of 80° C. At this condition, however, theradiator is 33% larger than at the optimal condition. Also, notice thatthe current densities range from 6.7 to 14.1 A/mm², which is much higherthan for conventional electric machines. The optimization also foundhigh torque density solutions at normal current densities, however,which indicates an increase in overall efficiency. In other words,decreasing the efficiency increases thermal losses, thus increasingradiator volume. For all optimizations the optimal magnet thickness was15 mm, which could be increased, but may approach manufacturing limits.

The optimal micro-hydrofoil array characteristic dimensions for theoptimal DWHX electric machine in this case study are presented in Table7:

TABLE 7 Optimal Micro-Hydrofoil Geometries for Best Case in initialsizing case study ΔT_(amb) 90 S_(t)/L_(c) 2.3 S_(l)/L_(c) 5 H/L_(c) 2.5L_(c) 0.2 N_(f, t) 61 N_(f, l) 27

These geometries can be used to make the optimal micro-hydrofoil arrayfor the specific machine identified by the optimization.

Example 2 Infinite Reservoir

In some applications, it may be practical to have a substantiallyinfinite thermal reservoir built into the system such as, for example,building water, a cooling pond, or external water cooling (e.g., usingintake water from a lake or ocean on a ship). The second case study,therefore, optimizes a DWHX electric machine for substantially infinitereservoir applications. This can be useful in situations where power andspeed outweigh efficiency to a certain extent such as, for example andnot limitation, offshore racing boats or Navy fast attack ships.

The infinite thermal reservoir can be modeled simply by fixing the fluidtemperature of the DWHX to the temperature of the infinite reservoir.The objective function can then be changed to consider only the volumeof the motor without regard to the volume of the pump and radiator. Thetwo temperatures that were simulated are 20° C. and 90° C. Thesetemperatures are typical for a large body of water and engine coolant,respectively. The results for each trial of the infinite reservoir studyare shown in Table 8:

TABLE 8 Fitness Function values for each trial in Infinite ReservoirCase Study T_(fluid) 20 90 Trial # Fitness Function Value 1 −381.0−289.1 2 −377.5 −289.5 3 −377.3 −288.7

Again, the optimization was performed three times to ensure the globalminimum was reached. In this case study the fitness function was withinfour points of the other trials. The results from this case study arepresented in Table 9:

TABLE 9 Optimization Results for Infinite Reservoir Case study T_(fluid)20 90 D [mm] 72.6 70.4 L [mm] 27.6 34 J [A/mm²] 25.9 20 EM Torque 105.782.9 Density [N-m/L] System Torque 48.9 38.4 Density [N-m/L] Efficiency83.2 88.7 Fitness Value −376.62 −289.67

The torque density based on motor volume is 48.9 N-m/L and 38.4 N-m/Lfor a fluid temperature of 20° C. and 90° C., respectively. The torquedensity based on electromagnetic volume is 105.7 N-m/L and 82.9 N-m/Lfor a fluid temperature of 20° C. and 90° C., respectively. 105.7 N-m/Lis a significant achievement for current density. Notice that thecurrent density of 25.9 and 20 A/mm², respectively, is significantlyhigher than typically current densities. Also, notice that theefficiencies are somewhat lower than the integrated radiator case, forexample, at 83.2 and 88.7 respectively. The optimization finds thesehigher current densities because it does not consider the extra heatrejection required by the resulting inefficiencies due to the ability ofthe infinite reservoir to reject basically limitless amounts of heat.This optimization provides for maximum power, yet still providesrelatively good efficiency. For comparison, a typical internalcombustion engine struggles to achieve 30% efficiency.

The optimal micro-hydrofoil array characteristic dimensions for thiscase study are presented in Table 10:

TABLE 10 Optimal Micro-Hydrofoil Geometries for Infinite Reservoir Casestudy T_(fluid) 20 90 S_(t)/L_(c) 2.2 2.2 S_(l)/L_(c) 5 5 H/L_(c) 2.52.5 L_(c) 0.2 0.2 N_(f, t) 47 51 N_(f, l) 27 33

In both case studies, the form factor of the electric machine was a“pancake style.” In other words, the depth of the machine was muchsmaller than its diameter. Also, as mentioned above, in the infinitereservoir study, the machine efficiencies were much lower than in theinitial sizing case study. The lower efficiencies are expected, however,because DWHX electric machines when coupled to an infinite reservoir ofcooling medium at a low temperature achieve such marked improvements incooling performance that more current can be forced into the windingleading to, simultaneously, extraordinary torque density and a slightlydiminished efficiency due to the increased thermal loss from the windingat the higher current levels. Typical machines could not sustainoperation under similar current loadings.

As a result, in the initial sizing case studies the optimization foundsolutions that were much more efficient due to the included radiatorsizing. In other words, lower efficiencies produce more heat that theradiator must reject, which leads to larger radiators. To satisfy thetradeoff between motor volume and radiator volume, therefore, theoptimization found motors with higher efficiencies. In the infinitereservoir case, on the other hand, because the infinite reservoir canreject large amounts of heat, less efficient, but higher current,solutions were found. Using the method described herein, the fitness canbe revised to, for example, minimize volume, mass, or other parameters,as desired.

In the initial sizing study the radiator volume was a weak function ofΔT_(amb) between 10° C. and 80° C. The results are replotted andnormalized against total system volume and displayed in FIG. 10. Noticethat the percentage volume of total system volume is a weak function ofΔT_(amb) between 10° C. and 80° C. indicating an optimal ratio of motorvolume to radiator volume for ΔT_(amb) between 10° C. and 80° C. Above80° C., however, radiator sizing can be reduced significantly due to theincreased driving force. It should be noted, however, that motor sizemust be increased to stay within the thermal limits.

The trends presented in the initial sizing study generally hold true forvarious power levels due mainly to the fact that the power of anelectric machine is substantially proportional to the volume of themachine. Also the trends hold true for other types of machine such asthose that do not have a rotor heat source such as, for example and notlimitation, an electric machine with an interior permanent magnet andswitched reluctance.

The increased thermal conductivity of the windings, combined with theproposed advanced cooling technology, enables high heat transfer rateswithout reaching the thermal limits of the wire insulation. Theincreased effective thermal conductivity of the windings, utilizingthermally conductive epoxy as the filler material, provides the sameorder of thermal conductivity as the core. In addition, while most ofthe heat from the machine is transferred into the DWHX, some of the heatstill travels to the frame. The increased thermal conductivity of thesystem, however, provides a reduced temperature drop from the windingsto the frame. This results in drastically increased frame temperatures.

The frame temperatures from the case studies presented above were ˜140°C., which exceeds the typical safe touch limit. This can nonetheless beeasily addressed with, for example and not limitation, proper framesizing (as discussed above), appropriate packaging, and materials. Intraction drive automotive applications, for example, the DWHX electricmachine may not be touch accessible, but may nonetheless be providedwith a “hot surface” warning label, for example, to warn techniciansduring maintenance.

Embodiments of the present invention comprise a novel advanced coolingtechnique, or direct winding heat exchanger (DWHX) comprising anadvanced heat exchanger placed proximate the winding bundles on thestator of an electric machine. This cooling technique can dramaticallyreduce the temperature and thermal resistance of the stator windings inmany concentrated winding electric machines. Embodiments of the presentinvention can also comprise an integrated design model. The model can beused in conjunction with particle swarm optimization, or otheranalytical methods, to perform initial sizing for, for example and notlimitation, electrical machines with integral radiator and infinitereservoir configurations. The system and method described herein providedramatic improvements in both efficiency and torque density in apractically manufacturable cooling system.

While several possible embodiments are disclosed above, embodiments ofthe present invention are not so limited. For instance, while severalpossible configurations of materials for the cooling system have beendisclosed, other suitable materials and combinations of materials couldbe selected without departing from the spirit of embodiments of theinvention. In addition, the location and configuration used for variousfeatures of embodiments of the present invention can be varied accordingto a particular motor size or power requirement that requires slightvariations due to, for example, the materials used and/or space or powerconstraints. In addition, the fitness functions described herein can bemodified to optimize different design parameters (e.g., volume or mass)for use in different applications. Such changes are intended to beembraced within the scope of the invention.

The specific configurations, choice of materials, and the size and shapeof various elements can be varied according to particular designspecifications or constraints requiring a device, system, or methodconstructed according to the principles of the invention. Such changesare intended to be embraced within the scope of the invention. Thepresently disclosed embodiments, therefore, are considered in allrespects to be illustrative and not restrictive. The scope of theinvention is indicated by the appended claims, rather than the foregoingdescription, and all changes that come within the meaning and range ofequivalents thereof are intended to be embraced therein.

What is claimed is:
 1. A system for cooling an electric machinecomprising a stator and one or more copper windings, the systemcomprising: one or more direct winding heat exchangers (DWHX) thermallycoupled to the one or more copper windings, each DWHX comprising: acoolant reservoir; and a plurality of micro-features disposed inside thecoolant reservoir; wherein a coolant flows through the one or more DWHXsto provide direct cooling to the one or more copper windings.
 2. Thesystem of claim 1, wherein the coolant reservoir comprises ameso-channel.
 3. The system of claim 1, wherein one or more of theplurality of micro-features comprise a micro-hydrofoil.
 4. The system ofclaim 1, wherein the plurality of micro-features are arranged in asymmetrical array about the centerline of the coolant flow.
 5. Thesystem of claim 1, wherein the coolant reservoir is substantiallyprismatic, and the plurality of micro-features are disposed only on oneor more of the major sides of the coolant reservoir.
 6. The system ofclaim 1, wherein each of the one or more DWHXs further comprises adovetail joint for detachably coupling the DWHX to a non-conductivebulkhead.
 7. The system of claim 1, further comprising a thermallyconductive epoxy disposed proximate the one or more DWHXs and the one ormore cooper windings for conducting heat therebetween.
 8. A system forcooling an electric machine comprising a stator, one or more end caps, aframe, and one or more copper windings, the system comprising: one ormore direct winding heat exchangers (DWHX) thermally coupled to the oneor more copper windings for providing direct cooling to the one or morecopper windings; an inlet plenum in fluid communication with the one ormore DWHXs for providing coolant to the one or more DWHXs; an outletplenum in fluid communication with the one or more DWHXs for removingcoolant from the one or more DWHXs; and a heat reservoir, in fluidcommunication with the inlet manifold and outlet manifold, for rejectingheat transferred to the coolant from the one or more DWHXs.
 9. Thesystem of claim 8, wherein the inlet plenum and the outlet plenum aredisposed in the one or more side covers.
 10. The system of claim 8,further comprising one or more non-conductive bulkheads for detachablycoupling the one or more DWHXs to the electric machine.
 11. The systemof claim 10, wherein the one or more DWHXs are pressed into the one ormore non-conductive bulkheads.
 12. The system of claim 11, wherein thenon-conductive bulkheads are pressed into the frame.
 13. The system ofclaim 8, wherein the heat reservoir comprises an integral radiator influid communication with the inlet plenum and the outlet plenum forshedding heat absorbed by the one or more direct winding heat exchangers(DWHX).
 14. The system of claim 8, wherein the heat reservoir comprisesa substantially infinite external radiator in fluid communication withthe inlet plenum and the outlet plenum for shedding heat absorbed by theone or more direct winding heat exchangers (DWHX).
 15. The system ofclaim 8, wherein each of the one or more DWHXs comprise: a coolantreservoir; and a plurality of micro-features disposed inside the coolantreservoir.
 16. The system of claim 15, wherein one or more of theplurality of micro-features comprise a micro-hydrofoil.
 17. The systemof claim 15, wherein the profile of each of the plurality ofmicro-features comprise one or more of the group consisting of square,round, or rhomboidal.